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I am interested in the interplay between mathematics and string theory. Previously, I have worked on problems that arose in the early days of mirror symmetry, such as expressing certain curve-count generating functions on given spaces in terms of oscillatory integrals over their mirror partners. The spaces I considered are flag varieties, classical objects in representation theory, which I find particularly interesting because they bring Langlands duality into the picture. In the process, I observed new, though still somewhat vague, connections to other areas. Gaining a better understanding of these connections will be my main focus while I am at IPMU.